Markov Chains

Markov Chains

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LF/604598171/R
Английский
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Draft November 3, 2018. 777 pages. Very good.Main subject categories: • Markov processes • Discrete-time Markov processes • Markov chains • Computational methods in Markov chains • AnalysisMathematics Subject Classification (2010): 60J05 Discrete-time Markov processes on general state spaces, 60-02 Research exposition (monographs, survey articles) pertaining to probability theory, 60B10 Convergence of probability measures, 60J10 Markov chains (discrete-time Markov processes on discrete state spaces), 60J22 Computational methods in Markov chains, 60F05 Central limit and other weak theoremsThis book covers the classical theory of Markov chains on general state-spaces as well as many recent developments. The theoretical results are illustrated by simple examples, many of which are taken from Markov Chain Monte Carlo methods. The book is self-contained, while all the results are carefully and concisely proven. Bibliographical notes are added at the end of each chapter to provide an overview of the literature.Part I lays the foundations of the theory of Markov chain on general states-space. Part II covers the basic theory of irreducible Markov chains on general states-space, relying heavily on regeneration techniques. These two parts can serve as a text on general state-space applied Markov chain theory. Although the choice of topics is quite different from what is usually covered, where most of the emphasis is put on countable state space, a graduate student should be able to read almost all these developments without any mathematical background deeper than that needed to study countable state space (very little measure theory is required).Part III covers advanced topics on the theory of irreducible Markov chains. The emphasis is on geometric and subgeometric convergence rates and also on computable bounds. Some results appeared for a first time in a book and others are original. Part IV are selected topics on Markov chains, covering mostly hot recent developments.
LF/604598171/R

Характеристики

ФИО Автора
Eric Moulines
Philippe Soulier
Pierre Priouret
Randal Douc
Язык
Английский
Серия
Springer Series in Operations Research and Financial Engineering
ISBN
9783319977034
Дата выхода
2018

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Markov Chains

Draft November 3, 2018. 777 pages. Very good.Main subject categories: • Markov processes • Discrete-time Markov processes • Markov chains • Computational met...

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